Название: Theory of Quantum Information with Memory
Автор: Mou-Hsiung Chang
Издательство: De Gruyter
Год: 2022
Страниц: 502
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Quantum information theory has now become a significant and important branch of scientific research. This is evidenced by its research activities during the last decade that have resulted in a huge body of literatures. However, a vast majority of these works have only focused on finite-dimensional and memoryless quantum channels without addressing increasingly important and yet realistic issues of infinite dimensionality and memory effects in quantum communication. This monograph is the first in a book form that addresses these two issues. It aims to give a systematic and mathematically rigorous treatment and to address the mathematical challenges that these two issues have posed.

This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infinite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.

This book is the product of a set of research notes that the author prepared during his study, learning and research on these two issues. Its content is largely based on the current account of relevant research results, published or not-yet-published, and contributed by many prominent researchers. The list of bibliography is certainly not exhaustive and is likely to have omitted works done by many researchers. The author apologizes for any inadvertent omissions of their works.

This book is intended to be as self-contained as possible in terms of mathematical prerequisites. With the exception of a few well-known theorems in functional analysis and operator theory that are stated in Chapter 1 without proofs, detailed proofs are provided for most of all other results for the reader’s convenience and for reader’s preparations in order to familiarize themselves with mathematical and theoretical aspects of the quantum information. On the other hand, mathematical topics are presented only if they will be used either as tools for rigorously treating relevant topics in quantum information or they will provide insights and motivations for extending the frontier in the field.